AC waveforms
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Resources and methods for learning about these subjects (list a few here, in preparation for your
research):
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Questions
Question 1
What is the difference between DC and AC electricity? Identify some common sources of each type of
electricity.
file 00028
Question 2
Alternating current produced by electromechanical generators (or alternators as they are sometimes
designated) typically follows a sine-wave pattern over time. Using a calculator, or a set of ”trig tables,” plot
a sine wave on the following graph:
+1
+0.5
0
-0.5
-1
0o
90o
180o
Rotation
file 00052
2
270o
360o
Question 3
Alternating current produced by electromechanical generators (or alternators as they are sometimes
designated) typically follows a sine-wave pattern over time. Plot a sine wave on the following graph, by
tracing the height of a rotating vector inside the circle to the left of the graph:
90o
0o
180o
270o
0o
90o
180o
270o
360o
To illustrate the principle here, I will show how the point is plotted for a rotation of 45o :
90o
45o
0o
o
180
270o
0o
45o
90o
180o
270o
360o
You may wish to use a protractor to precisely mark the angles along the rotation of the circle, in making
your sine-wave plot.
file 00093
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Question 4
Define the following terms:
•
•
•
•
•
Frequency
Wavelength
Cycle
Hertz
Amplitude
file 00043
Question 5
Apply the following terms to this graph of an AC voltage measured over time:
•
•
•
•
Frequency
Period
Hertz
Amplitude
+10 V
+5 V
0V
-5 V
-10 V
0
10 ms
20 ms 30 ms
Time
40 ms
file 00054
Question 6
Frequency used to be expressed in units of cycles per second, abbreviated as CPS. Now, the standardized
unit is Hertz. Explain the meaning of the obsolete frequency unit: what, exactly, does it mean for an AC
voltage or current to have x number of ”cycles per second?”
file 00053
Question 7
If an AC voltage has a frequency of 350 Hz, how long (in time) is its period?
file 00055
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Question 8
Determine the frequency of a waveform having a period of 1.4 milliseconds (1.4 ms).
file 03276
Question 9
Radio waves are comprised of oscillating electric and magnetic fields, which radiate away from sources
of high-frequency AC at (nearly) the speed of light. An important measure of a radio wave is its wavelength,
defined as the distance the wave travels in one complete cycle.
Suppose a radio transmitter operates at a fixed frequency of 950 kHz. Calculate the approximate
wavelength (λ) of the radio waves emanating from the transmitter tower, in the metric distance unit of
meters. Also, write the equation you used to solve for λ.
file 01819
Question 10
If the only instrument you had in your possession to detect AC voltage signals was an audio speaker,
how could you use it to determine which of two AC voltage waveforms has the greatest period?
FUNCTION GENERATOR
Hz
1
10 100 1k 10k 100k 1M
Speaker
coarse
fine
DC
output
FUNCTION GENERATOR
Hz
1
coarse
fine
10 100 1k 10k 100k 1M
DC
output
file 00387
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Answers
Answer 1
DC is an acronym meaning Direct Current: that is, electrical current that moves in one direction only.
AC is an acronym meaning Alternating Current: that is, electrical current that periodically reverses direction
(”alternates”).
Electrochemical batteries generate DC, as do solar cells. Microphones generate AC when sensing sound
waves (vibrations of air molecules). There are many, many other sources of DC and AC electricity than
what I have mentioned here!
Answer 2
+1
+0.5
0
-0.5
-1
0o
90o
180o
270o
360o
Rotation
Answer 3
90o
0o
180o
270o
0o
6
90o
180o
270o
360o
Answer 4
These terms are very easy to find definitions for, from a wide variety of sources. I’ll let you discover
what they mean for yourself!
Answer 5
Frequency = 50 Hz
+10 V
+5 V
Amplitude
(peak)
0V
-5 V
Period
20 ms
-10 V
0
10 ms
20 ms 30 ms
Time
40 ms
Answer 6
Each time an AC voltage or current repeats itself, that interval is called a cycle. Frequency, being
the rate at which an AC voltage or current repeats itself over time, may be represented in terms of cycles
(repetitions) per second.
Answer 7
Period = 2.8571 milliseconds
Answer 8
f = 714.29 Hz
Answer 9
λ ≈ 316 meters
I’ll let you find the equation on your own!
Answer 10
Connecting the speaker to each AC voltage source, one at a time, will result in two different audio tones
output by the speaker. Whichever tone is lower in pitch is the waveform with the greatest period.
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Notes
Notes 1
Discuss a bit of the history of AC versus DC in early power systems. In the early days of electric power
in the United States of America, there was a heated debate between the use of DC versus AC. Thomas
Edison championed DC, while George Westinghouse and Nikola Tesla advocated AC.
It might be worthwhile to mention that almost all the electric power in the world is generated and
distributed as AC (Alternating Current), and not as DC (in other words, Thomas Edison lost the AC/DC
battle!). Depending on the level of the class you are teaching, this may or may not be a good time to explain
why most power systems use AC. Either way, your students will probably ask why, so you should be prepared
to address this question in some way (or have them report any findings of their own!).
Notes 2
For many students, this might be the first time they realize trigonometry functions have anything to
do with electricity! That voltage and current in an AC circuit might alternate according to a mathematical
function available in their calculators is something of a revelation. Be prepared to discuss why rotating
electromagnetic machines naturally produce such waveforms. Also, encourage students to make the cognitive
connection between the independent variable of a sine function (angle, expressed in units of degrees in this
question) to actual shaft rotation in a real generator.
Notes 3
For many students, this might be the first time they realize trigonometry functions have anything to
do with electricity! That voltage and current in an AC circuit might alternate according to a mathematical
function available in their calculators is something of a revelation. Be prepared to discuss why rotating
electromagnetic machines naturally produce such waveforms. Also, encourage students to make the cognitive
connection between the independent variable of a sine function (angle, expressed in units of degrees in this
question) to actual shaft rotation in a real generator.
Notes 4
The unit ”Hertz” is an example of how an implicitly defined label like ”cycles per second” (CPS) came
to be replaced by one having no objective meaning at all. Similar to how ”Celsius” replaced ”Centigrade” as
the official metric name for a unit of temperature measurement. Pardon me for stepping up on my soapbox
here, but changes such as these really irritate me.
It is important to understand that these terms apply to non-electrical phenomena as well as electrical.
The wide applicability of such terms allows for easier comprehension. Ask your students to give common
examples of these terms in everyday life. Hint: music is an excellent context for this question!
Notes 5
As always, it is more important to be able to apply a term to a real-life example than it is to memorize
a definition for that term. In my experience, many students prefer to memorize definitions for terms rather
than to go through the trouble of understanding how those terms apply to real life. Make sure students
realize just how and why these AC terms apply to a waveform such as this.
Notes 6
Encourage your students to discuss the origins of the new unit (Hertz), and how it actually communicates
less information about the thing being measured than the old unit (CPS).
Notes 7
It is important for students to realize the reciprocal relationship between frequency and period. One is
cycles per second while the other is seconds per cycle.
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Notes 8
It is important for students to realize the reciprocal relationship between frequency and period. One is
cycles per second while the other is seconds per cycle.
Notes 9
I purposely omit the velocity of light, as well as the time/distance/velocity equation, so that students
will have to do some simple research this calculate this value. Neither of these concepts is beyond high-school
level science students, and should pose no difficulty at all for college-level students to find on their own.
Notes 10
An audio speaker is an outstanding instrument to use in teaching AC theory, because it makes use
of a human sense that most instruments do not. I have constructed a simple headphone-based listening
instrument for my own lab use, and have found it invaluable, especially in the absence of an oscilloscope.
There is so much the trained ear may discern about an AC waveform based on volume and tone!
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